At first the problem of formal analysis only. We proceed with the talk of instances and concern ourselves first with relations of inclusion and exclusion. The question is as to membership of a class, and the dominant formula is the dictum de omni et nullo. Until the view of the individual units with which we are so far familiar has undergone radical revision, the primary inquiry must be into the forms of a class-calculus. Individuals fall into groups in virtue of the possession of certain predicates. Does one group include, or exclude, or intersect another with which it is com pared? We are clearly in the field of the diagrams of the older text-books, and much of the phraseology is based upon an origi nal graphic representation in extension. The middle term, though conceived as an intermediary or linking term, gets its name as intermediate in a homogeneous scheme of quantity, where it cannot be of narrower extension than the subject nor wider than the predicate of the conclusion. It is also, as Aristotle adds, middle in position in the syllogism that concludes to a universal affirmative. Again so long as we keep to the syllogism as complete in itself and without reference to its place in the great structure of knowledge, the nerve of proof cannot be conceived in other than a formal manner. In 'analytic we work with an ethos differ ent from that of dialectic. We presume truth and not proba bility or concession, but a true conclusion can follow from false premises, and it is only in the attempt to derive the premises in turn from their grounds that we unmask the deception. The passage to the conception of system is still required. The Prior Analytics, then, are concerned with a formal logic to be knit into a system of knowledge of the real only in virtue of a formula which is at this stage still to seek. The forms of syllogism, how ever, are tracked successfully through their figures, i.e., through the positions of the middle term that Aristotle recognizes as of actual employment, and all their moods, i.e., all differences of affirmative and negative, universal and particular within the figures, the cogent or legitimate forms are alone left standing, and the formal doctrine of syllogism is complete. Syllogism already defined becomes through exhibition in its valid forms clear in its principle. It is a speech-and-thought-form in which certain mat ters being posited something ether than the matter posited neces sarily results because of them, and though it still needs to receive a deeper meaning when presumed truth gives way to necessary truth of premises, the notion of the class to that of the class concept, collective fact to universal law, its formal claim is manifest. "Certain matters being posited." Subject and predicate not already seen to be conjoined must be severally known to be in relation with that which joins them, so that more than one direct conjunction must be given. "Of necessity." If what are to be conjoined are severally in relation to a common third, it does perforce relate or conjoin them. "Something other." The conjunction was by hypothesis not given, and is a new result by no means to be reached, apart from direct perception save by use of at least two given conjunctions. "Because of them," therefore. Yet so long as the class-view is prominent there is a suggestion of begging of the question. The class is either consti tuted by enumeration of its members, and passing by the diffi culty involved in the thought of "its" members, is an empirical universal of fact merely, or it is grounded in the class-concept. In the first case it is a formal scheme which helps knowledge and the theory of knowledge not at all. We need then to develop the alternative, and to pass from the external aspect of all-ness to the intrinsic ground of it in the universal, which, whatsoever the assistance it receives from induction in some sense of the word, in the course of its development for the individual mind, is secured against dependence on instances by insight into the systematic nexus of things. The conception of linkage needs to be deepened by the realization of the middle term as the ground of nexus in a real order which is also rational.
Aristotle's solution of the paradox of inference, viz., of the fact that in one sense to go beyond what is in the premises is fallacy, while in another sense not to go beyond them is futility, lies in his formula of implicit and explicit, potential and actual.
The real nexus underlying the thought-process is to be articulated in the light of the voucher by intelligence as to the truth of the principles of the various departments of knowledge which we call sciences, and at the ideal limit it is possible to transform syllogism into systematic presentation, so that, differently written down, it is definition. But for human thought sense, with its accidental setting in the matter itself incognizable, is always with us. The activity of thought is never so perfectly realized as to merge implication in intuition. Syllogism must indeed be ob jective, i.e., valid for any thinker, but it is also a process in the medium of individual thinking, whereby new truth is reached. A man may know that mules are sterile and that the beast before him is a mule, yet believe her to be in foal "not viewing the several truths in connection." The doctrine, then, that the uni versal premise contains the conclusion not otherwise than poten tially is with Aristotle cardinal. The datum of sense is only retained through the universal. It is possible to take a universal view with some at least of the particular instances left uninvesti gated. Recognition that the class-concept is applicable may be independent of knowledge of much that it involves. Knowledge of the implications of it does not depend on observation of all members of the class. Syllogism as formula for the exhibition of truth attained, and construction or what not as the instru mental process by which we reach the truth, have in writers since Hegel and Herbart tended to fall apart. Aristotle's view is other. Both are syllogisms, though in different points of view. For this reason, if for no other, the conception of movement from the potential possession of knowledge to its actualization remains indispensable. Whether this is explanation or description, a problem or its solution, is of course another matter.
In the Posterior Analytics the syllogism is brought into decisive connection with the real by being set within a system in which its function is that of material implication from principles which are primary, immediate and necessary truths. Hitherto the as sumption of the probable as the true rather than as what will be conceded in debate has been the main distinction of the standpoint of analytic from that of dialectic. But the true is true only in reference to a coherent system in which it is an immediate ascertainment of thought or to be deduced from a ground which is such. The ideal of science or demonstrative knowledge is to exhibit as flowing from the definitions and postu lates of a science, from its special principles, by the help only of axioms or principles common to all knowledge, and these not as premises but as guiding rules, all the properties of the subject matter, i.e., all the predicates that belong to it in its own nature. In the case of any subject-kind, its definition and its existence being avouched by thought, "heavenly body" for example, the problem is, given the fact of a non-self-subsistent characteristic of it, such as the eclipse of the said body, to find a ground which expressed the cause in virtue of which the adjectival concept can be exhibited as belonging to the subject-concept in the strict sense. We are under the necessity, then, of revising the point of view of the syllogism of all-ness. We discard the con ception of the universal as a predicate applicable to a plurality, or even to all, of the members of a group. The exhaustive judg ment, if attainable, could not be known to be exhaustive. The universal is the ground of the empirical "all" and not conversely. A formula such as the equality of the interior angles of a triangle to two right angles is only scientifically known when it is not of isosceles or scalene triangle that it is known, nor even of all the several types of triangle collectively, but as a predicate of triangle recognized as the widest class-concept of which it is true, the first stage in the progressive differentiation of figure at which it can be asserted.